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Homework Help: Complex numbers problem

  1. Mar 7, 2006 #1
    need a lil help here

    thnx
     
    Last edited: Mar 7, 2006
  2. jcsd
  3. Mar 7, 2006 #2

    benorin

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    Set g(z)=z, that is, write 2 + zi = z and then solve for z.
     
  4. Mar 7, 2006 #3
    ok.. thanks, any tips in solving for z?

    i got.. z = 2 + zi
    z/z = 2/z + i
    1 = 2/z + i
    2/z = 1 - i
    z= 2/(1-i)

    dont think im going the right way
     
    Last edited: Mar 7, 2006
  5. Mar 7, 2006 #4

    benorin

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    [tex]2 + iz = z[/tex]
    [tex]2 = z -iz = z(1-i)[/tex]

    and so, like you have

    [tex] z= \frac{2}{1-i}[/tex]

    now multiply by the conjugate of the denominator on top and bottom
     
  6. Mar 7, 2006 #5
    wel..... we can divide 2 by (1 - i) to get z...


    OHHHhhhhhhhhhhhhhhhhhhhh ahhhhhhhhhh.!!!1 forgot that!1 multiple by conjugate... how silly of me

    thankyou so much!!!! !!!!!!1

    yaaay.....

    bottom: (1-i) * (1+i) = 2
    top: 2*(1+i) = 2+2i

    = (2+2i)/2
    = 1+i

    Yayaya Thnnx So mUcH!
     
    Last edited: Mar 7, 2006
  7. Mar 7, 2006 #6

    benorin

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    [tex] z= \frac{2}{1-i} =\left( \frac{2}{1-i}\right) \left( \frac{1+i}{1+i} \right) = \frac{2(1+i)}{(1-i)(1+i)} = \frac{2(1+i)}{1^2-i^2} = \frac{2(1+i)}{1-(-1)} = 1+i[/tex]
     
  8. Mar 7, 2006 #7
    nice diagram!

    tankyou somuch
     
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